(untitled) (Journal of Mathematical Study, 2018)
Let F be a non-empty formation of groups, τ a subgroup functor and H a p-subgroup of a finite group G. Let G=G/H_G and H =H/H_G. We say that H is F_τ-s-supplemented in G if for some subgroup T and some τ-subgroup S of G contained in H, HT is subnormal in G and H ∩ T ≤ SZ_F (G). In this paper, we investigate the influence of F_τ-s-supplemented subgroups on the structure of finite groups. Some new characterizations about solubility of finite groups are obtained.